Temperature, Magnetic Field, and Dimensionality Effects on the Raman Spectra of TaSe$_2$

In bulk form, TaSe$_2$ exhibits transitions between commensurate and incommensurate charge-density wave (CDW) phases, and is attracting interest for advanced device applications. In order to explore the evolution of the groundstate CDW phase with layer number, mechanical exfoliation of bulk crystals provides few- to single-layer flakes. In the present work, we extend our opto-thermal Raman measurements\footnote{R. Yan, J. R. Simpson, \textit{et al.}, ACS Nano \textbf{8}, 986 (2014).} on MoS$_2$ to include other TMDs, specifically TaSe$_2$, in both $1T$ and $2H$ crystallographic phases. A novel, magneto-Raman microscope system affords measurement of low-frequency (down to 10\,cm$^{-1}$) vibrational modes as a function of both temperature (100 to 400)\,K and magnetic field (0 to 9)\,T. The dependence of the observed Raman-active phonons on temperature and magnetic field will be discussed and compared with earlier results on MoS$_2$. Specifically, we observe the appearance of low-frequency, zone-folded modes in the CDW state, which soften with temperature similar to the higher frequency, in-plane $E_{2g}$ mode. Additionally, we compare the measured magneto-Raman results to calculations using \textit{ab initio}, density functional theory.